Question

For the given graph of $y=\tan 2x;\forall x\in R$
Select the correct statements.

Answer 1

Given the graph of $\tan 2x\forall x\in R$


As clear from the graph, $\tan x$ is not defined at values which are odd multiples of $\pi /4$
So, it's domain will be:
$R-(2n+1)\frac{\pi }{2}\forall n\in Z$

Now, coming to periodicity, we can find it either from the graph itself or by using the expression.

1st method:

As per the graph of $\tan 2x$ the value is getting repeated after every $\frac{3\pi }{4}-\frac{\pi }{4}=\frac{\pi }{2}$


2nd Method:

Now, using the fact that if $f\left(x\right)$ has a period $T$,
then $f(ax+b)$ will have a period $\frac{T}{|a|}.$

Using the same concept. we know $\tan x$ has a fundamental period $\pi$
$\Rightarrow \tan 2x$ will have a fundamental period $\pi /2$